Infinite Arccotangents Equals One Arctangent

Geometry Level 4

\[ \text{arccot} \left(1^2 + \dfrac34\right) + \text{arccot} \left(2^2 + \dfrac34\right) + \text{arccot} \left(3^2 + \dfrac34\right) + \text{arccot} \left(4^2 + \dfrac34\right) + \cdots = \, ? \]

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